变系数非线性二阶周期边值问题的正解  

Positive Solutions of Nonlinear Second-Order Periodic Boundary Value Problems with Variable Coefficient

作　　者：姚庆六[1] 

机构地区：[1]南京财经大学应用数学系,南京210003

出　　处：《应用数学学报》2008年第3期564-573,共10页Acta Mathematicae Applicatae Sinica

摘　　要：利用锥上的不动点指数定理考察了变系数非线性二阶周期边值问题的正解.主要定理表明,只要非线性项在某些有界集合上的增长速度是适当的,该问题就具有n个正周期解,其中n是一个任意的自然数.The positive solutions are considered for a nonlinear second-order periodic boundary value problem with variable coefficient by applying the fixed point index theorems on cone. The main results show that the problem has n positive periodic solutions provided the growth rates of nonlinear term on some bounded sets are appropriate, where n is an arbitrary natural number.

关 键 词：二阶常微分方程 周期边值问题 正解 存在性 多解性 

分 类 号：O175.8[理学—数学]